phi (201212) and phi (111111)

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April 3rd 2012, 01:28 PM
Wachoorou

phi (201212) and phi (111111)

What are the values of phi (201212) and phi (111111)?
April 4th 2012, 04:53 AM
a tutor

Re: phi (201212) and phi (111111)

$\phi(n)=n\Pi_{p|n}\left(1-\frac{1}{p}\right)$

So for example

$\phi(30)=\phi(2\times 3 \times 5)=30\times\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right) \left(1-\frac{1}{5}\right)=8$ .

So factorise your numbers..

Yes 269 is prime.(Wink)
April 4th 2012, 06:00 AM
Wachoorou

Re: phi (201212) and phi (111111)

I don't know how to use the symbols and I meant to say sigma function, not phi. So it would be sigma (201212) and sigma (111111)?
April 4th 2012, 06:29 AM
a tutor

Re: phi (201212) and phi (111111)

Since sigma is a multiplicative function $\sigma(mn)=\sigma(m)\sigma(n)$ where gcd(m,n)=1.

So for example, $\sigma(180)=\sigma(4)\sigma(9)\sigma(5)=(1+2+4) (1+3+9) (1+5)= 546$

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